Historical Volatility Estimates from Close and Intraday Prices

Summary

The document briefly discusses historical volatility estimation using close-to-close returns and price ranges. It identifies standard deviation of historical returns as a basic close-price approach and mentions range-based estimators that use high and low prices, including Parkinson’s and Garman–Klass methods. The central comparison is that range-based measures can use more information within a trading period than closing prices alone.

The answer is incomplete: its displayed standard-deviation expression is not a clear, complete volatility formula, and it does not provide the detailed open-close expression requested. It cautions that range-based methods rely on assumptions such as continuous trading and available high and low observations, and may underestimate volatility when those assumptions do not hold. No data, estimator derivations, sampling choices, or empirical comparisons are supplied, so the discussion is an introduction rather than a full calculation guide.

Key ideas

• Close-to-close historical volatility is based on the dispersion of returns calculated from closing prices.
• Range-based estimators use intraperiod high and low prices.
• Range-based approaches rely on assumptions about trading continuity and observed price ranges.
• The document does not give complete formulas or an empirical comparison of estimators.

Tags

# Close Volatility - Open-Close Volatility


# Close Volatility - Open-Close Volatility












Could anyone please give the detailed expression of either the close-close or open-close volatility ?

Thanks

## Answer by Con Fluentsy (score -1, accepted)

https://quant.stackexchange.com/a/59316

Standard deviation method Historical price returns also on close prices

stdev = historical = sqrt[(x- (sum x/n))^2]

The simplest method for Parkinson's High Close method is

The high Low method is statistically more efficient than the standard close method. However it assumes continuous trading and observations of high and Low prices. The method can therefore underestimate the true volativity.

The Garman Klass High Low Close Method, can once again underestimate volatity

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.